= Open-shell Systems : U-TD-DFT and spin-adapted TD-DFT for spin-conserving excitations =

== U-TD-DFT ==

Using a UKS reference in SCF, the input for U-TD-DFT reads:
{{{
$TDDFT
IMETHOD 
 2
ISF
 0
...
$END
}}}

== X-TD-DFT ==

Using a ROKS reference in SCF, the input for Spin-adapted TD-DFT (X-TD-DFT) can be set in two ways. 

One uses U-TD-DFT solver to solve the X-TD-DFT  in '''spin-orbit''' basis ['''recommended! for efficiency, since integral-direct algorithm has been implemented''']:
{{{
$TDDFT
IMETHOD 
 2
ISF
 0
...
icorrect
1
itest
1
itrans
1
$END
}}}
The option ''itrans'' will transform the eigenvector in CV(aa),CV(bb) basis into CV(0) and CV(1) basis.

The other one uses the original spin-adapted TD-DFT solver to solve the X-TD-DFT  in '''spin-tensor''' basis ['''This is just for MO-based algorithm, which requires the TRAINT section for integral transformations, and hence not recommended for large applications''']:
{{{
$TDDFT
imethod
3
isf
0
...
itest
1
icorrect
1
$END
}}}

These two ways give exactly '''the same''' excitation energies. The only different is the representation if "itrans" is not used.